Birds have overcome the problem of sleeping in risky situations by developing the ability to sleep with one eye open and one hemisphere of the brain awake. Such unihemispheric slow-wave sleep is in direct contrast to the typical situation in which sleep and wakefulness are mutually exclusive states of the whole brain. We have found that birds can detect approaching predators during unihemispheric slow-wave sleep, and that they can increase their use of unihemispheric sleep as the risk of predation increases. We believe this is the first evidence for an animal behaviourally controlling sleep and wakefulness simultaneously in different regions of the brain.